Preface; 1. Vectors and Matrices; 2. Solving Linear Equations Ax = b; 3. The Four Fundamental Subspaces; 4. Orthogonality; 5. Determinants and Linear Transformations; 6. Eigenvalues and Eigenvectors; 7. The Singular Value Decomposition (SVD); 8. Learning from Data; Appendix 1. The Ranks of AB and A + B; Appendix 2. Eigenvalues and Singular Values: Rank One; Appendix 3. Counting Parameters in the Basic Factorizations; Appendix 4. Codes and Algorithms for Numerical Linear Algebra; Appendix 5. Matrix Factorizations; Appendix 6. The Column-Row Factorization of a Matrix; Appendix 7. The Jordan Form of a Square Matrix; Appendix 8. Tensors; Appendix 9. The Condition Number; Appendix 10. Markov Matrices and Perron-Frobenius; Index; Index of Symbols; Six Great Theorems / Linear Algebra in a Nutshell.
From Gilbert Strang, a new approach to linear algebra that is suitable for everyone, going from basics to the singular value decomposition.
Gilbert Strang has been teaching Linear Algebra at Massachusetts Institute of Technology (MIT) for over fifty years. His online lectures for MIT's OpenCourseWare have been viewed over ten million times. He is a former President of the Society for Industrial and Applied Mathematics and Chair of the Joint Policy Board for Mathematics. Professor Strang is the author of twelve books, including the bestselling classic Introduction to Linear Algebra (2016), now in its fifth edition.
'The author certainly makes every effort to explain all the concepts in great detail with well-chosen examples, and he provides a huge number of problems including 'challenge problems' and 'recommended problems'. There are also extensive web resources available.' Peter Giblin, University of Liverpool, The Mathematical Gazette